2(a+4)=4a(2a+4)

Solution for 2(a+4)=4a(2a+4) equation:

Simplifying
2(a + 4) = 4a(2a + 4)

Reorder the terms:
2(4 + a) = 4a(2a + 4)
(4 * 2 + a * 2) = 4a(2a + 4)
(8 + 2a) = 4a(2a + 4)

Reorder the terms:
8 + 2a = 4a(4 + 2a)
8 + 2a = (4 * 4a + 2a * 4a)
8 + 2a = (16a + 8a2)

Solving
8 + 2a = 16a + 8a2

Solving for variable 'a'.

Combine like terms: 2a + -16a = -14a
8 + -14a + -8a2 = 16a + 8a2 + -16a + -8a2

Reorder the terms:
8 + -14a + -8a2 = 16a + -16a + 8a2 + -8a2

Combine like terms: 16a + -16a = 0
8 + -14a + -8a2 = 0 + 8a2 + -8a2
8 + -14a + -8a2 = 8a2 + -8a2

Combine like terms: 8a2 + -8a2 = 0
8 + -14a + -8a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -7a + -4a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -7a + -4a2)' equal to zero and attempt to solve:

Simplifying
4 + -7a + -4a2 = 0

Solving
4 + -7a + -4a2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1 + 1.75a + a2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.75a + 1 + a2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.75a + a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.75a + a2 = 0 + 1
1.75a + a2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.75a + a2 = 1

The a term is 1.75a.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75a + 0.765625 + a2 = 1 + 0.765625

Reorder the terms:
0.765625 + 1.75a + a2 = 1 + 0.765625

Combine like terms: 1 + 0.765625 = 1.765625
0.765625 + 1.75a + a2 = 1.765625

Factor a perfect square on the left side:
(a + 0.875)(a + 0.875) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(a + 0.875) equal to 1.328768227 and -1.328768227.

Subproblem 1
a + 0.875 = 1.328768227

Simplifying
a + 0.875 = 1.328768227

Reorder the terms:
0.875 + a = 1.328768227

Solving
0.875 + a = 1.328768227

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.875' to each side of the equation.
0.875 + -0.875 + a = 1.328768227 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + a = 1.328768227 + -0.875
a = 1.328768227 + -0.875

Combine like terms: 1.328768227 + -0.875 = 0.453768227
a = 0.453768227

Simplifying
a = 0.453768227

Subproblem 2
a + 0.875 = -1.328768227

Simplifying
a + 0.875 = -1.328768227

Reorder the terms:
0.875 + a = -1.328768227

Solving
0.875 + a = -1.328768227

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.875' to each side of the equation.
0.875 + -0.875 + a = -1.328768227 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + a = -1.328768227 + -0.875
a = -1.328768227 + -0.875

Combine like terms: -1.328768227 + -0.875 = -2.203768227
a = -2.203768227

Simplifying
a = -2.203768227

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.453768227, -2.203768227}
Solution
a = {0.453768227, -2.203768227}